In a semiconductor exposure apparatus such as a stepper, alignment is performed in such a manner that a circuit pattern that has been formed on a reticle (mask) will be overlaid highly precisely on a circuit pattern that has been formed on a wafer (plate) serving as a substrate.
A technique referred to as AGA (Advanced Global Alignment) is known as a method of obtaining an array of circuit pattern areas (shots) that have been formed on a wafer. AGA is a technique that includes the steps of selecting several sample shots from all available shots, measuring amounts of deviation of the positions of these sample shots from a design position and subjecting the results of the measurement to statistical processing to thereby obtain wafer compensation parameters for compensating for the shot array on the wafer. The wafer compensation parameters mentioned here are the following quantities, by way of example:
(1) shift error of wafer center position (amount of translation) (Swx, Swy);
(2) wafer (shot array) rotation error (amount of rotation) (θwx, θwy); and
(3) wafer (shot array) magnification error (amount of linear expansion and contraction) (βwx, βwy).
Further, the difference (θwx−θwy) between the X and Y components of the amount of wafer rotation is referred to as “wafer orthogonality”.
In order to improve the precision of alignment, there has recently been proposed a method of applying a correction by obtaining the amount of deformation of a shot per se in addition to finding wafer compensation parameters. It is considered that the causes of shot deformation are device-related, such as distortion of the exposure lens, and process-related, such as deformation of the wafer due to heating. The following quantities can be mentioned as parameters (referred to as “shot compensation parameters”) for correcting for shot deformation (i.e., shot shape error):
(1) shot rotation error (amount of rotation) (θsx, θsy); and
(2) shot magnification error (amount of linear expansion and contraction) (βsx, βsy).
The relationship between wafer compensation parameters and shot compensation parameters is illustrated in FIGS. 1 and 2, in which FIG. 1 is a diagram illustrating the relationship between wafer magnification and shot magnification. In FIG. 1, WafD indicated by the dashed line represents the designed external shape of the wafer, and WafR indicated by the solid line represents, in exaggerated form, the external shape of the wafer in a case where the wafer has undergone expansion and contraction caused by thermal deformation, or the like. Let radial expansion of the wafer in the X and Y directions be represented by βwx and βwy, respectively, in a standard coordinate system (x,y), the origin of which is a reference point on the wafer stage of the stepper. Wafer magnification has an effect upon the shot array. In FIG. 1, the manner in which the center position of each shot deviates in the outward direction from the designed coordinates is indicated by the arrows assigned to the shots. Further, SframeD represents the designed external shape of a shot, and SframeR represents the external shape of the shot brought about when shot magnification error occurs. Shot expansion is represented by βsx, βsy in the standard coordinate system (x,y).
FIG. 2 is a diagram illustrating the relationship between wafer rotation and shot rotation. Here WafR represents, in exaggerated form, the external shape of the wafer in a case where the wafer has been rotated relative to the standard coordinate system (x,y) of the stage. Let the amount of rotation of the wafer in the X and Y directions be represented by θwx, θwy, respectively, in a standard coordinate system the center of which is a reference point on the wafer stage of the stepper. FIG. 2 illustrates a case where θwx=θwy holds, indicating the orthogonality (angular deviation) of the wafer and stage is zero. Wafer rotation has an influence upon the shot array. Further, SframeD represents the designed external shape of the shot, and SframeR represents the shape of the shot that has developed an error in orthogonality owing to shot deformation. In FIG. 2, rotation of the axes of the shot in the standard coordinate system (x, y) is represented by θsx, θsy.
With the AGA method, the amount of deviation of the shot reference position (usually the shot center) from the designed value is found by measuring the positions of alignment marks assigned within the shot. In this case, marks to be measured within the shot constitute one set, namely one shot in each of the X and Y directions. FIG. 3A illustrates an instance where marks MX1, MY1 have been disposed in a shot (SHOT).
On the other hand, in a case where a shot compensation parameter for correcting for shot deformation is found, measurement is performed upon disposing a greater number of marks (MX1 to MX3, MY1 to MY3), i.e., greater than the single set of one mark for each of the X and Y directions. A method of finding shot compensation parameters is disclosed in Japanese Patent Application Laid-Open No. 09-266164.
The general shot compensation alignment method will be described with reference to FIG. 4, which is a block diagram illustrating an off-axis wafer alignment system in a semiconductor exposure apparatus. This alignment system includes a reticle 401; a projection exposure optical system 402; an image storing arithmetic unit 403 for subjecting a provided image signal to various image processing and storing the image signal and results of processing; a prealignment unit 406 for adjusting coarse wafer orientation based upon a wafer external-shape reference when the wafer has been sent to the alignment system from a wafer transport apparatus (not shown); a computer terminal 407 for accepting a command input from a user; a wafer 408 that is to be aligned, a microscope 404 for enlarging and observing the image of a pattern formed on a wafer 408; a CCD camera 417 for converting the pattern image of the wafer 408, which has been obtained by the microscope 404, to an electric signal and supplying the signal to the image storing arithmetic unit 403; an XY stage 410 for moving the coordinate position of the wafer 408 in the direction of a plane and in a direction perpendicular to the plane; a wafer chuck 409 for holding the wafer 408 on the XY stage 410; a monitor 411 serving as a display mechanism by which the user checks the image provided by the microscope 404; and a controller 405 for controlling each of the above-mentioned elements. The controller 405 has a memory 420 and a CPU. The microscope 404 and CCD camera 417 are referred to as an off-axis observation optical system. In FIG. 4, it is assumed that the positions of the reticle 401 and projection exposure optical system 402 have been decided accurately by a method such as the FRA method and that the relative positional relationship (base line) among the projection exposure optical system 402 and off-axis observation optical system 404, 417 has already been measured.
As shown in FIG. 3C, measurement sample shots S1, S2 for calculating shot compensation parameters and measurement sample shots S3 to S6 for calculating wafer compensation parameters have been formed on the wafer 408. Alignment marks shown in FIG. 3B have been formed in each of measurement sample shots S1 to S6. In the measurement sample shots S1, S2, marks MX1 to MX3, MY1 to MY3 are the object of measurement for alignment. In the measurement sample shots S3 to S6, marks MX1, MY1 are the object of measurement for alignment.
FIG. 5 is a flowchart illustrating processing of the conventional technique for shot compensation alignment. The conventional technique will be described with reference to the flowchart of FIG. 5.
At step S501 in FIG. 5, wafer 408 is carried into the exposure apparatus by a wafer transport apparatus (not shown), the wafer 408 is positioned coarsely by prealignment unit 406, and then the wafer 408 is transported to the XY stage 410. The wafer 408 is held on the XY stage 410 by vacuum suction applied by the wafer chuck 409.
Steps S502 to S505 constitute a procedure for automatically measuring shot compensation parameters.
More specifically, step S502 calls for drive of the XY stage 410 to be controlled in such a manner that the alignment mark MX1, which has been formed in the first measurement shot S1, will enter the field of view of the microscope 404.
Next, at step S503, deviation of the mark position is detected. This deviation is detected as follows: First, the microscope 404 and CCD camera 417 capture the pattern of the alignment mark MX1, which is illuminated by an alignment illumination device (not shown), as an image signal. By using pattern matching, the controller 405 compares the pattern of the alignment mark stored in the image storing arithmetic unit 403 with the image that has been captured by the CCD camera 417 and calculates deviation l×1 from the designed position of the alignment mark MX1.
This is followed by step S504, at which it is determined whether steps S502, S503 have been executed for all sample shots (S1, S2). If an unprocessed shot remains, control returns to step S502. If unprocessed shots do not remain, control proceeds to step S505. Specifically, the remaining alignment marks MX2, MX3, MY1 to MY3 in the first measurement shot S1 are measured through a procedure similar to that for MX1, and positional deviations lxn, lyn (n=1 to 3, where n is assigned based upon the mark number) of each mark in the x and y directions are measured.
If the positional deviation of each mark has been measured (“YES” at step S504) for all sample shots, then the shot compensation parameters are calculated at step S505. A method of calculating shot compensation parameters is as follows:
Shot compensation parameters are found for each shot of the sample shots S1 to S4. The designed position of each mark that resides in the shot is represented by (dxn,dyn) (n=1 to 3), where the center of the shot is taken as the origin. The mark position (dxn′,dyn′) compensated for by the shot compensation parameters is expressed as follows by Equation (1):
                              (                                                                      dxn                  ′                                                                                                      dyn                  ′                                                              )                =                                            [                                                                                          1                      +                                              β                        ⁢                                                                                                  ⁢                        sx                                                                                                                                                -                        θ                                            ⁢                                                                                          ⁢                      sy                                                                                                                                  θ                      ⁢                                                                                          ⁢                      sx                                                                                                  1                      +                                              β                        ⁢                                                                                                  ⁢                        sy                                                                                                        ]                        ⁢                          (                                                                    dxn                                                                                        dyn                                                              )                                +                      (                                                            Ssx                                                                              Ssy                                                      )                                              (        1        )            where Ssx, Ssy represent amounts of shift error of the shot center. Further, the actual position of the measured mark is expressed as follows by Equation (2):
                              (                                                    dxn                                                                    dyn                                              )                +                  (                                                    lxn                                                                    lyn                                              )                                    (        2        )            
A compensation residual V is expressed as follows by Equation (3):
                                                        V              =                            ⁢                                                1                  m                                ⁢                                                      ∑                                          n                      =                      1                                        m                                    ⁢                                                                                                                                    (                                                                                                                    dxn                                                                                                                                                    dyn                                                                                                              )                                                +                                                  (                                                                                                                    lxn                                                                                                                                                    lyn                                                                                                              )                                                -                                                  (                                                                                                                                                      dxn                                  ′                                                                                                                                                                                                                      dyn                                  ′                                                                                                                                              )                                                                                                            2                                                                                                                          =                            ⁢                                                1                  m                                ⁢                                                      ∑                                          n                      =                      1                                        m                                    ⁢                                                                                                                                    (                                                                                                                    lxn                                                                                                                                                    lyn                                                                                                              )                                                -                                                                              [                                                                                                                                                                β                                    ⁢                                                                                                                                                  ⁢                                    sx                                                                                                                                                                                                              -                                      θ                                                                        ⁢                                                                                                                                                  ⁢                                    sy                                                                                                                                                                                                                                    θ                                    ⁢                                                                                                                                                  ⁢                                    sx                                                                                                                                                                        β                                    ⁢                                                                                                                                                  ⁢                                    sy                                                                                                                                                        ]                                                    ⁢                                                      (                                                                                                                            dxn                                                                                                                                                              dyn                                                                                                                      )                                                                          +                                                  (                                                                                                                    Ssx                                                                                                                                                    Ssy                                                                                                              )                                                                                                            2                                                                                                          (        3        )            
Since lxn, lyn, dxn, dyn are already known, it will suffice to obtain {Ssx, Ssy, θsx, θsy, βsx, βsy} by solving simultaneous equations that minimize V. Here it will suffice to use a shot array in which shifts Ssx, Ssy of the shot array have been found as the result of calculating wafer compensation parameters of fth-degree step, and therefore it is not necessary to use the value found here in subsequent compensating drive. As the result of measuring a plurality of sample shots, the number of shot compensation parameters obtained is equivalent to the number of sample shots. By subsequently taking the average of these parameters, therefore, shot compensation parameters of the wafer are obtained.
Steps S506 to S509 constitute a procedure for calculating wafer compensation parameters. This method is the aforementioned AGA technique.
Step S506 calls for the controller 405 to drive the XY stage 410 in such a manner that the alignment mark MX1, which has been formed in the first sample shot S3 for wafer measurement, will enter the field of view of the microscope 404.
Next, at step S507, the mark position is detected. The method of detecting mark position is similar to that of step S503 above. Deviation lxk (k=3 to 6, where k is assigned based upon the sample-shot number) from the designed position of the alignment mark MX1 is calculated at step S507.
This is followed by step S508, at which it is determined whether steps S506, S507 have been executed for all sample shots (S3 to S6). If an unprocessed shot remains, control returns to step S506. If unprocessed shots do not remain, control proceeds to step S509. Specifically, the remaining alignment mark MY1 in the first measurement shot S3 is measured through a procedure similar to that for MX1, and a positional deviation lyk of the mark in the Y direction is calculated. Further, the processing of steps S506, S507 is repeated with regard to all sample shots (S3 to S6), and lxk, lyk (k=3 to 6) are found for every sample shot.
If the positional deviations of each of the marks are found for all sample shots (“YES” at step S508), then the wafer compensation parameters are calculated at step S509. A method of calculating wafer compensation parameters is as follows:
First, deviations (lxk,lyk) of the reference position (usually the position of the shot center) of each sample shot from the designed value are found. Coordinates obtained by adding the measured deviations (lxk,lyk) of the alignment marks to the designed positions of the marks from the center position of the sample shot are the coordinates of the actual mark position.
Deviations (Lxk,Lyk) from the center position of the shot are found by taking the average of these values. The designed position of the center of each sample shot that resides in the wafer is represented by (Dxk,Dyk). A shot-center position (Dxk′,Dyk′) compensated for by the wafer compensation parameters is expressed as follows by Equation (4):
                              (                                                                      Dxk                  ′                                                                                                      Dyk                  ′                                                              )                =                                            [                                                                                          1                      +                                              β                        ⁢                        wx                                                                                                                        -                                              θ                        ⁢                        wy                                                                                                                                                        θ                      ⁢                      wk                                                                                                  1                      +                                              β                        ⁢                        wy                                                                                                        ]                        ⁢                          (                                                                    Dxk                                                                                        Dyk                                                              )                                +                      (                                                            Swk                                                                              Swk                                                      )                                              (        4        )            
Further, the actual position of the shot center obtained as the result of measurement is expressed as follows by Equation (5):
                              (                                                    Dxk                                                                    Dyk                                              )                +                  (                                                    Lxk                                                                    Lyk                                              )                                    (        5        )            
A compensation residual V is expressed as follows by Equation (6):
                                                        V              =                            ⁢                                                1                  m                                ⁢                                                      ∑                                          k                      =                      1                                        m                                    ⁢                                                                                                                                    (                                                                                                                    Dxk                                                                                                                                                    Dyk                                                                                                              )                                                +                                                  (                                                                                                                    Lxk                                                                                                                                                    Lyk                                                                                                              )                                                -                                                  (                                                                                                                                                      Dxk                                  ′                                                                                                                                                                                                                      Dyk                                  ′                                                                                                                                              )                                                                                                            2                                                                                                                          =                            ⁢                                                1                  m                                ⁢                                                      ∑                                          k                      =                      1                                        m                                    ⁢                                                                                                                                    (                                                                                                                    Lxk                                                                                                                                                    Lyk                                                                                                              )                                                -                                                                              [                                                                                                                                                                β                                    ⁢                                                                                                                                                  ⁢                                    wx                                                                                                                                                                        -                                                                          θ                                      ⁢                                      wy                                                                                                                                                                                                                                                                        θ                                    ⁢                                                                                                                                                  ⁢                                    wx                                                                                                                                                                        β                                    ⁢                                                                                                                                                  ⁢                                    wy                                                                                                                                                        ]                                                    ⁢                                                      (                                                                                                                            Dxk                                                                                                                                                              Dyk                                                                                                                      )                                                                          +                                                  (                                                                                                                    Swx                                                                                                                                                    Swy                                                                                                              )                                                                                                            2                                                                                                          (        6        )            
Since Lxk, Lyk, Dxk, Dyk are already known, it will suffice to obtain {Swx, Swy, θwx, θwy, βwx, βwy} by solving simultaneous equations that minimize V.
If shot compensation parameters and wafer compensation parameters have been found, each unit of the exposure apparatus is driven (subjected to compensating drive) at step S510 in accordance with these compensation parameters so as to diminish the error between the shot array and shot shape.
Finally, control proceeds to step S511 to carry out exposure.
By repeating steps S501 to S511 for all wafers to be exposed, it is possible to perform the exposure of each shot with a high overlay precision in accordance with the compensated shot array and shot shape.
The minimum required number of marks to calculate the wafer compensation parameters in a shot is one set for X and Y (one X measurement mark and one Y measurement mark, or one X-Y measurement mark).
However, the number of alignment marks that must be measured within a shot in order to find shot compensation parameters is greater than one set for X and Y. In accordance with Equation (3), at least three sets of alignment marks for X, Y must be measured in order to independently calculate all of the shot compensation parameters {θsx, θsy, βsx, βsy, Ssx, Ssy}.
With the conventional alignment method of measuring and compensating for shot compensation parameters automatically, it is necessary to perform measurements at sample shots and alignment marks for calculation of shot compensation parameters on a wafer-by-wafer basis. As a result, measurement is performed at many sample shots and alignment marks for each and every wafer. A problem which results is a decline in throughput.